Variable | Description |
|
|
β | Sound level |
λ | Wavelength |
ω | Angular frequency |
ρ | Density of medium |
B | Bulk modulus of elasticity |
f | Frequency |
I | Sound intensity |
k | Angular wave number |
s | Longitudinal displacement at x and t |
sm | Longitudinal amplitude |
t | Time |
v | Speed of sound in medium (Sound Waves), or |
Wave speed (Transverse Waves, Longitudinal | |
| Waves) |
x | Position |
y | Transverse displacement at x and t |
ym | Transverse amplitude |
|
|
Reference: 3.
Transverse Waves (15,1)
Equations:
y = ym ⋅ SIN(k ⋅ x – ω ⋅ t) | v = λ ⋅ f | 2 | ⋅ π | ω = 2 ⋅ π ⋅ f |
k = | ||||
|
|
| λ |
|
Example:
Given: ym=6.37_cm, k=32.11_r/cm, x=.03_cm, ω=7000_r/s, t=1_s.
Solution: f= 1114.0846_Hz, λ=0.0020_cm, y=2.6655_cm, v=218.0006_cm/s.
Longitudinal Waves (15, 2)
Equations:
s = sm ⋅ COS(k ⋅ x – ω ⋅ t) | v = λ ⋅ f | 2 | ⋅ π | ω = 2 ⋅ π ⋅ f |
k = | ||||
|
|
| λ |
|
Example:
Given: sm=6.37_cm, k=32.11_r/cm, x=0.03_cm, ω=7000_r/s, t=1_s.
Solution: s=5.7855_cm, v=2.1800_m/s, λ=0.1957_cm, f=1114.08456_Hz.
Equation Reference